A video package prepared by CNN Tuesday on the jailhouse death of Sandra Bland failed to note that the woman had recently claimed to have been struggling with post traumatic stress disorder and mild depression — a seemingly important detail as the 28-year-old’s family challenges the claim by Texas authorities that she committed suicide in her cell.

Police say that Bland, who was arrested on July 10 and found dead three days later, hung herself with a plastic garbage bag from inside her...